Production & Use of X-rays (Cambridge International A-Level Physics)

Production of X-rays

• X-rays are short wavelength, high-frequency part of the electromagnetic spectrum

  • They have wavelengths in the range 10⁻⁸ to 10⁻¹³ m

• X-rays are produced when fast-moving electrons rapidly decelerate and transfer their kinetic energy into photons of EM radiation

Producing X-rays

• At the cathode (negative terminal), the electrons are released by thermionic emission
• The electrons are accelerated towards the anode (positive terminal) at high speed
• When the electrons bombard the metal target, they lose some of their kinetic energy by transferring it to photons
• The electrons in the outer shells of the atoms (in the metal target) move into the spaces in the lower energy levels
• As they move to lower energy levels, the electrons release energy in the form of X-ray photons
• When an electron is accelerated, it gains energy equal to the electronvolt; this energy can be calculated using:

$E_{max}=eV$

• This is the maximum energy that an X-ray photon can have
• Therefore, the maximum X-ray frequency f_max, or the minimum wavelength λ_min, that can be produced is calculated using the equation:

$E_{max}=eV=hf_{max}=\frac{hc}{λ_{min}}$

Maximum frequency: $f_{max}=\frac{eV}{h}$

Minimum wavelength: $λ=\frac{hc}{eV}$

• Where:

  • e = charge of an electron (C)
  • V = voltage across the anode (V)
  • h *= *Planck’s constant (J s)
  • c = speed of light (m s^-1)

Worked Example A typical spectrum of the X-ray radiation produced by electron bombardment of a metal target is shown below.

Explain why:

(a) a continuous spectrum of wavelengths is produced.

(b) the spectrum has a sharp cut-off at short wavelengths.

Answer:

Part (a)

• Photons are produced whenever a charged particle is accelerated towards a metal target
• The wavelength of the photons depends on the magnitude of the acceleration
• The electrons which hit the target have a distribution of accelerations, therefore, a continuous spectrum of wavelengths is observed

Part (b)

• The minimum wavelength is equal to

$λ_{min}=\frac{hc}{E_{max}}$

• This equation shows the maximum energy of the electron corresponds to the minimum wavelength

  • Therefore, the higher the acceleration, the shorter the wavelength

• At short wavelengths, the sharp cut-off occurs as each electron produces a single photon, so, all the electron energy is given up in one collision

Using X-rays in Medical Imaging

• X-rays have been highly developed to provide detailed images of soft tissue and even blood vessels

• When treating patients, the aims are to:

  • reduce the exposure to radiation as much as possible
  • improve the contrast of the image

Reducing exposure

• X-rays are ionising, meaning they can cause damage to living tissue and can potentially lead to cancerous mutations

• Therefore, healthcare professionals must ensure patients receive the minimum dosage possible

• In order to do this,aluminium filters are used

  • This is because many wavelengths of X-ray are emitted
  • Longer wavelengths of X-ray are less penetrating which means they are more likely to be absorbed by the body
  • This means they do not contribute to the image and pose more of a health hazard
  • The aluminium sheet absorbs these long wavelength X-rays making them safer

Contrast and sharpness

• Contrast is defined as: The difference in the degree of blackening between structures

• Contrast allows a clear difference between tissues to be seen

• Image contrast can be improved by:

  • using the correct level of X-ray hardness: hard X-rays for bones, soft X-rays for tissue
  • using a contrast media

• Sharpness is defined as: How well-defined the edges of structures are

• Image sharpness can be improved by:

  • using a narrower X-ray beam
  • reducing X-ray scattering by using a collimator or lead grid
  • smaller pixel size